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⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⣼⣿⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠛⠋⠘⣿⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢿⡿⠋⠀⢠⣤⣤⠀⢻⣇⠀⠀⠸⣿⣿⠀⠀⣿⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠰⣯⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⠀⠀⣠⣤⣴⣴⣾⣿⢀⣀⣾⣶⣲⣿⣿⣿⣾⣷⣿⣾⣿⣾⣿⣶⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⡭⠉⠈⠉⠀⠀⢤⠀⠀⠻⠿⠟⠀⢸⣿⠀⠀⠀⠈⢀⣴⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢠⣼⡗⠀ ⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣟⣉⠉⢻⣿⠃⠀⠀⠘⢿⠀⠀⠉⠙⢿⣿⣿⡟⠋⠛⠻⣿⣿⣿⢿⣿⡆⠀⢈⣩⣼⣿⣿⣟⡛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣇⣀⣶⣧⣤⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⣠⣶⣿⣿⡿⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⡏⠀⢨⣿⡇⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⢿⣿⡶⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀⡀⠀⠀⠉⠉⠈⣿⣿⣤⣾⠿⠏⠀⠀⠤⢁⢻⣿⣷⡀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⠿⠿⠿⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⡿⠀⠀⢻⣿⠇⠀ ⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⢸⣿⠃⠀⠀⠀⠀⠀⠸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠙⣿⣿⡁⠀⢀⠈⢲⡔⠂⢿⣸⣿⣦⣀⣠⣄⣀⠘⠛⢿⣿⡇⣠⣶⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⣽⡿⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠋⠀⡀⠀⢂⠌⠀⣠⣽⣿⣿⣿⣧⡈⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⡟⠀⠀⢸⣿⠇⠀⠀ ⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣶⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⢀⠀⠄⢉⠠⣤⣿⡟⠋⢿⣿⣿⣿⣦⡀⠀⠸⣿⣧⠀⠀⠀⠀⠀⣀⣤⣶⣿⣟⣛⣭⣵⡿⠟⠋⠀⠘⣿⣿⣿⣿⣿⠟⠿⣿⠛⠁⠀⠀⠀⢀⣾⣿⠀⠀⠀⣸⣿⠀⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠈⠉⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⢠⣶⣿⡿⠉⢀⠀⠠⠀⠌⢲⣿⡿⠀⠀⣀⣭⣍⣽⣿⡅⠀⠀⠙⢿⣷⣄⣠⣶⣿⣿⠿⠻⠿⠛⠉⠉⠁⠀⠀⠀⣤⣾⡿⠉⠁⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⢰⣿⡏⠀⠀⠀ ⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠀⢀⠀⢄⠠⡀⣼⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠇⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠤⣾⣿⡏⠀⠀⠀⠉⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣻⣿⣿⣦⣤⣴⣿⣿⣏⣨⠅⣹⣿⣿⣿⣿⣿⣿⣿⠄⠀⢀⠀⢌⠰⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⠛⣿⣿⣿⣦⣴⣾⣿⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⢁⣀⣤⣶⣤⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⣿⣤⣀⣀⣀⣀⡀⠀⠀⣀⣀⣴⣷⣿⠿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣯⡄⢂⠀⠠⢈⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡿⠛⣿⣿⣿⡉⠻⣿⣿⣿⠆⣿⣿⣿⠿⢿⣿⣿⣿⣿⠇⠀⠀⢀⣾⣿⠟⢿⣿⠀⠀⠀⢀⣶⣿⣿⣿⠿⠟⠛⠋⢉⣿⣯⣴⡆⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⠃⠀⣼⣿⡿⣿⣿⣿⣿⣿⡿⢿⣽⣿⣏⣾⣿⣿⣷⠀⢆⣄⣿⣿⢫⣴⣾⣿⡿⣍⣬⣿⣇⡀⠀⠈⠀⠀⢹⣿⣿⣷⣦⣽⣿⣿⣧⣿⡟⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⢈⣿⡟⠀⢸⣿⡄⠀⢀⣿⡿⠋⠁⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⢻⣿⣷⣠⣿⣿⡇⢠⣰⣞⣿⣿⣿⢿⣿⣿⣿⣅⡀⣻⣿⣿⣿⣿⣿⣿⣜⣼⣿⣿⠋⠀⢹⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⡏⠁⢻⣿⣿⣿⠙⣿⣷⣿⡀⣀⣤⣾⣿⠁⠀⠀⠀⣾⣿⠇⠀⠈⠙⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠠⠈⠿⣿⣿⣿⣿⣇⣣⣿⣿⣿⣿⣿⣿⣎⣙⣻⣿⣿⣿⣿⣿⡿⢁⠙⣿⣿⣿⣿⠇⠀⠀⠸⢿⣿⣿⡿⠟⣿⣿⣿⣿⣦⢈⣿⣿⡟⠁⠀⢸⣿⣿⣿⠀⠀⠉⣿⡟⠛⣻⣿⠃⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢠⣁⠠⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣂⢼⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⣻⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⢿⣿⣶⣿⠇⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣌⠧⡑⠀⢾⣿⣿⣿⣿⣿⡟⣿⣿⣿⡏⢹⣿⡉⠉⢹⣿⣿⣿⣿⣿⣌⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣧⠀⠀⠨⣿⣿⠃⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⡖⣀⢈⣿⣿⣿⠿⠿⣿⣿⣌⡉⣩⣷⣿⣿⣷⣤⣠⣉⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣦⡀⠀⠀⢠⣿⡏⠀⢸⣿⠀⠀⠐⣿⣏⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⡐⠀⢸⣿⣿⡏⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠟⢻⣿⣿⣿⣿⣿⣇⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡇⠀⠈⣿⣇⠀⠀⢸⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⡀⠙⢿⣿⣧⡴⠂⠐⢢⡀⠀⣀⠅⠆⠶⠶⣦⡆⠀⣠⣾⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⡧⡄⠀⠙⣿⣆⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠁⠠⠚⢉⢻⣿⣷⣦⠃⡀⠄⠁⠈⠀⠀⠀⠀⠨⣤⣄⣿⣿⣿⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⣤⠀⠀⠀⠀⠀⢀⣿⡗⡗⠀⠀⠸⣿⣦⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡈⠠⣀⠻⠾⠿⠻⣿⣿⣄⡁⠈⠒⢦⣤⣄⣤⣤⣴⣿⣿⣿⠋⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣺⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣾⣿⡇⠁⠀⠀⠀⠈⢿⣷⣄⠘⢿⣦⣠⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠁⠄⠀⢀⠀⠀⡘⢿⣿⣿⣶⡀⠈⠻⠿⢿⣿⣿⣿⡿⣿⣦⡄⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⢈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠈⠀⡀⠐⠀⠀⢹⣿⣿⣤⡙⠀⣠⣾⡿⢿⣿⣇⠸⢿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⡀⠁⠀⡀⠂⠁⠰⡿⢿⣿⣿⣿⣿⣿⠃⢘⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣴⣿⣿⣿⡿⠿⢿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣿⡿⠉⠹⢿⣿⣷⣤⣤⣴⣤⣦⣴⣦⣄⣌⠉⠉⡁⢀⣤⣿⣿⣇⢈⣩⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⢻⣿⣿⡿⠛⠿⢿⣿⣿⣥⡀⠀⠀⠀⠀⢨⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⠁⠠⠀⠀⠈⣻⣿⣏⣹⣍⠉⠛⠿⠿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⣷⣶⣤⣿⣿⣿⣷⣤⣁⣀⣿⡟⢿⣷⣦⣴⣶⢾⡿⢿⣷⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⡀⠄⠁⠀⠼⣿⣷⠈⣿⣆⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣧⣄⡈⣿⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣶⣶⣿⣿⡅⠀⠀⠀⣸⣿⣿⡏⠻⣿⣿⣿⣾⣿⠀⠀⠹⣿⣄⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡁⠀⢀⠈⡀⠂⠈⣿⣿⡆⠈⠻⣿⣤⣀⣀⡀⠀⢀⣨⣿⣿⣿⣿⣧⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣷⣤⣤⢿⣿⣿⡀⠀⢸⣿⠋⠙⣿⡆⠀⠀⠘⠿⣷⣄⣀⠀⠘⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠐⠠⠒⠀⣀⣲⣿⣿⣿⡆⠠⢈⠛⢿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⠿⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⡿⣿⣿⠏⠀⠈⠙⠻⣿⣿⣿⣷⣆⣸⣿⠀⠀⠘⣿⣆⠀⠀⠀⠉⠛⢿⣷⣤⣿⡟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠄⠀⡀⠀⠂⣹⣿⣿⣿⣿⣇⠀⢈⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢀⣰⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⢡⣿⡿⠀⠀⠀⠀⠀⠙⢿⣿⣟⣿⣿⣿⠀⠀⠀⠹⣿⣤⡀⠀⠀⠀⠈⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡂⠀⢀⠐⣥⣿⣿⠋⢸⣿⠏⠀⣬⣾⣿⠿⣿⣯⡉⠉⢩⣽⣿⣿⣿⣿⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⠙⢿⣶⣤⡀⠀⠈⢿⣷⣶⣤⡀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣴⣿⣿⣁⣶⣾⡿⠃⢠⣿⣿⡇⠀⠙⣿⣷⣴⣿⠟⠋⠛⠻⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠈⠛⣿⡀⠀⣼⣿⠉⠙⢿⣷⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⠟⢻⣿⣟⠀⠀⢘⣿⣿⣿⣦⡐⣻⣿⣿⠇⠀⢀⠀⢀⠀⠈⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⢻⣇⠀⣿⡿⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡧⣿⣿⠂⠀⠛⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⠛⠁⠀⠠⠀⠠⠀⠀⠂⢀⠘⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⠘⠻⢿⣾⣿⣇⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⢻⣿⣇⠀⠀⢸⣿⣿⣿⠋⠀⣿⣿⡿⠁⠀⠀⠂⢀⠁⠂⠂⠁⠠⠀⢀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠁⠀⠀⠀⠉⢻⣿⣿⣿⠀⠀⠀⢺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠈⣿⣿⡄⠀⠀⠹⣿⣷⣄⢢⣿⣿⣶⣦⣤⠁⡀⠀⠠⠐⠀⠠⠁⢀⠀⠈⠐⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⢿⣿⣆⠀⠀⣿⣿⣯⣿⣿⠃⠈⠙⠿⣿⣶⣤⠁⠀⠐⠀⠠⠀⠀⠌⠀⢎⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠿⣿⣷⡀⠈⢀⠀⠁⠀⢂⣮⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⢀⠀⠄⠀⠉⠉⠉⠁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣦⣀⣆⣡⠌⣢⡟⢘⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠠⢀⠂⢀⠐⠀⢨⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢸⣷⣼⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠈⢀⠰⠀⠀⣀⠂⣸⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣷⠀⠈⡉⠣⢋⡿⣖⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠠⠀⢀⠀⠁⠀⠠⢼⣿⣿⡀⠀⠀⣠⣴⣿⠟⠉⠁⠈⠈⠄⠂⠁⠀⠠⣈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⡀⠐⠀⡀⢈⣐⢀⣈⣿⣿⣃⣴⣿⡟⠋⠁⠀⡀⠂⠁⡌⠀⠀⠂⣱⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠄⠀⠐⣾⣿⣿⣿⣿⠟⠻⣿⣧⡀⠈⢀⠀⠀⠁⢀⠠⣡⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣦⣤⡀⢀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠠⠈⠀⠀⠀⠀⢿⣿⡄⠀⠙⢿⣷⣤⠀⠀⠌⠀⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠛⠿⠿⢿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⢺⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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/‾‾‾‾‾‾‾‾‾‾‾\ / \ | [₍ᐢ..ᐢ₎] | \ o o o / -----------------

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⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⢸⠀⣼⣆⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠈⠞⣿⣿⣿⣿⢟⠋⠀⢿⠀⠉⡟⢸⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢹⡀⠂⠀⡰⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠣⡄⡾⠀⠀⠀⢸⠀⢿⣍⠢⡀⠠⣔⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⢸⠀⢐⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⡠⠊⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⠶⠞⠁⠀⠀⠀⢸⢂⠘⡎⠢⢭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⣦⠃⠜⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡜⠃⢠⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⢀⡀⠀⢰⢸⠈⠀⢹⣄⠀⢐⣦⢴⣶⣦⢤⣤⣀⠀⠀⢀⣀⠀⠀⠀⢀⠟⡎⠁⢸⠀⠀⡀⠀⠀⡴⣾⣷⣶⣶⣶⣦⣤⡉⠀⣤⣿⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢃⡄⣼⠀⠀⠀⢸⠡⠃⢸⣿⣶⣾⣿⠯⣿⡿⡿⣮⢞⢝⣠⠈⠈⠉⠓⠢⢼⣼⣿⢗⡮⠞⠉⠀⠀⢸⢿⣟⢿⢏⠽⢿⠝⢿⣷⣾⣿⣿⠁⠀⠀⡠⡴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠦⠾⠁⠀⠀⠀⢸⠀⠀⠸⣿⣯⣿⠁⣯⣯⢿⣜⢿⢷⠕⣽⢆⠀⠀⠀⠀⠀⠙⡝⠚⠀⠀⠀⠀⢠⢗⠝⡫⡄⢑⢜⢅⡽⣕⢿⣾⣿⡇⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣸⠀⠀⢠⣿⣿⡿⠄⣿⣿⣽⣛⣷⡱⣿⢡⠝⡢⣄⡀⠀⠀⣀⡷⡄⠀⠀⢀⡴⣻⣢⣕⢅⢎⡣⡱⠗⣵⣫⢿⣾⣿⡿⠈⢀⠢⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⣉⣉⠁⠀⠀⣿⠀⠀⡎⣿⣿⣿⡻⣿⣏⢏⢟⣵⢽⣗⡹⣊⠢⣁⠝⣷⣾⡁⡇⢩⡶⣾⢟⢞⣷⣓⣟⡣⡳⡮⢊⢎⢿⣾⣿⣿⣿⣧⢇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣦⣴⠇⠀⠀⠀⣿⠀⢠⣾⣿⣿⣷⣿⣟⣯⣣⠳⢻⣎⣞⢣⢎⡢⢑⡒⠍⠘⠑⡇⢹⣟⠣⣿⣯⡫⣣⣜⢷⣝⣉⢵⣱⣷⣹⡿⢸⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⣿⣿⣿⣿⣷⡏⠐⠣⡰⣩⢚⡷⢱⠯⡴⠝⠀⠀⠰⡄⡇⣸⡟⠘⡷⡗⡕⣝⠟⠃⢍⣳⡣⠾⠟⠋⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠ ⠀⠀⠀⢠⢿⡇⢀⡏⠀⠀⡇⠀⠀⠙⣿⣿⣷⣿⣧⡶⣿⡻⠋⠊⠔⠉⠀⠀⠀⠀⣠⢶⡇⡇⣿⣿⣿⣫⣮⣪⠻⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠀ ⠀⠀⣰⢫⢸⡇⣌⠀⠀⠀⡇⠀⠀⠀⣘⠻⣿⣷⣫⠿⠯⠀⠀⠀⠀⠀⠠⣳⣢⢾⣿⣿⡇⡇⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠔⢈⣼⣿⡿⠃⠀⠀⠀⠀⠀⠠⢋⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠈⢀⠟⣿⣿⣦⢀⡀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡇⡇⣿⣿⣷⣤⡀⢀⡀⠀⠀⠀⢀⡀⠔⠹⣿⡿⡅⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠀⠀⠀⠀⠀⠸⣆⠈⠻⠁⠀⢨⢶⣦⡈⠙⢯⡙⠦⠤⠀⢀⠉⡏⢁⠠⠤⠔⠋⣡⠞⠉⢩⣽⠿⣆⠀⠀⠉⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⠀⠀⠀⠙⣦⡀⠀⣴⣿⡸⣿⣆⡂⡈⡟⠷⠴⢂⣄⡀⡇⣀⣔⠢⠴⢿⣃⣴⣾⣿⠏⢸⣿⢆⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⢈⡆⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⡎⠀⠀⠀⢰⠅⠉⢾⣿⣿⣳⡈⠿⡌⠘⠚⠀⣀⢤⠈⠙⠛⠉⣀⡀⠀⠈⠉⣀⠿⠃⢠⡾⠃⣸⠟⠁⠀⠀⠀⠴⣆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠ ⢸⠀⠀⠀⠀⠀⣀⣴⠞⠀⠀⢸⡃⠀⠠⡞⠉⠀⠀⢸⣿⣿⡕⣵⣤⡛⠵⣰⠋⠀⠎⠀⡀⡀⠀⢣⠀⠑⡴⠪⠊⢀⣴⠟⠁⣰⡇⠀⠀⠀⠀⠎⡠⠋⠀⠀⠀⠀⠀⠀⣠⢎⠔⠅ ⠸⣴⡦⡀⣠⡾⠋⠋⠀⠀⠀⠃⣃⠤⢡⡖⠀⡀⠀⢨⣿⣿⣷⡈⠻⣯⣢⣽⣦⢚⣆⢡⢸⣿⢰⣀⢦⣔⣡⣠⣾⡿⠃⣠⣾⣿⠃⡎⠑⠐⠁⢸⣃⠃⠀⠀⠀⠀⢀⡔⠟⢉⠄⠀ ⠈⢿⣿⣿⢿⢀⠀⠀⠀⠀⡘⠀⠉⠀⠐⡀⢂⡴⠞⢫⣿⣿⣿⣿⣦⡈⠻⣿⣄⠋⠙⢻⠘⣿⡜⠗⠀⢈⣥⡿⠋⣠⣾⣿⣿⣿⢿⣦⡀⠀⠀⠈⠀⠀⡀⠀⠀⠜⠋⠀⢀⡘⠀⠀ ⠀⠉⠉⠁⢸⠁⢇⠀⠀⠸⠁⠀⠀⢀⠾⣿⠋⡠⠚⣩⣾⣿⣿⣿⣿⣿⣦⡈⠻⢿⣢⣿⣮⣿⣓⣴⡾⠛⠁⣠⣾⣿⣿⣿⣿⡟⢧⠙⣿⢦⡀⠀⠀⣠⠁⠲⠔⠀⠀⠀⠆⠀⠀⠀ ⠀⢀⣀⣀⠈⠹⢬⣀⣤⠇⠀⠀⣠⣿⣯⠃⡜⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⣁⠀⡇⠉⠉⣀⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠱⡊⢷⣭⡒⠮⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀

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⠀⠀⠤⢤⣤⣤⡤⠀⠀⠀⠀⠄⠀⠀⠀⢠⡤⣤⣤⡄⡄⢠⡄⠀⠀⠀⠀⠀⠠⢤⣤⣤⠀⠠⣄⣤⢠⣤⡄⢤⣤⣤⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢀⢀⣤⣰⣆⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣼⣿⣿⡟⠉⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⡲⣭⢻⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢻⡟⠃⢃⡌⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡵⣋⢮⡽⠉⣤⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠈⣇⢿⡝⢻⠀⠂⠄⣰⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⢫⠞⡜⡇⢗⣻⠿⣫⠝⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣹⠀⣀⠘⣎⢾⣼⡀⠀⣰⣿⠀⣿⠀⠀⠀⣠⠀⣴⠀⠚⢻⡇⠀⢿⣆⢀⠀⠀⠀⠀⠀ ⠀⠀⢋⠞⡱⣱⠸⣾⣿⢧⠿⣜⣛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠃⢠⠀⢹⣷⣿⣿⣿⣮⣟⡳⣼⡿⠋⣳⣿⣷⠎⣁⠀⠀⠕⣇⣀⣄⢥⡀⠀⢻⠛⠂⠀⠀⠀⠀ ⠀⠀⠈⡜⡱⠠⠇⢿⣯⢿⡿⣬⣝⡾⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣿⠖⠚⠦⡤⠤⠴⠿⢿⣟⠻⣿⣶⣯⢛⣯⣅⠸⠋⠈⠹⡷⡋⡛⢮⣾⣿⣿⣿⣷⣼⣭⣽⣸⡶⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠡⠘⡘⣿⣿⢯⣹⣾⣽⣧⢻⡜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠈⢿⣀⠀⡀⢿⠀⠀⡢⡎⠫⠁⠙⠛⠛⢯⡏⠁⠀⠠⠁⠀⠁⠭⠡⣺⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠥⠀⠀⢡⢹⣿⢻⣽⠙⠻⣿⣶⣝⠮⢱⠢⣄⠀⠀⠀⠀⠀⠀⣼⡁⠘⠀⠠⢹⣶⣿⣿⣿⢫⠝⠃⠰⠄⢀⣀⡄⠙⠃⠈⡖⡇⠀⢈⠔⠊⠙⡷⠋⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠅⠀⠀⠂⢿⡏⣭⡄⠀⠈⠛⢿⣿⣽⢦⠉⠗⢦⣦⡄⠀⠀⢳⢸⣿⣒⣠⣟⠟⠙⠛⢷⣶⠬⠤⠄⣀⡄⠸⠉⠀⢀⠀⢸⢠⠘⣩⠀⠀⠰⠀⣤⡿⠟⠋⡏⢹⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠈⠜⣿⡲⣧⠀⠀⠀⠀⠙⠿⣿⣗⣜⠤⡀⠸⠷⡀⠈⢧⣿⣿⣟⣿⠿⡓⠶⠿⣿⡅⠀⠀⠰⢯⠀⠎⣁⠀⠀⣸⠇⠀⠺⣤⣠⣦⣾⣿⠀⠀⠀⣴⡌⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠸⣷⠻⣥⡀⠀⠀⠀⠀⠘⣿⣿⡑⣤⡔⢤⠙⠦⢀⠀⡀⡄⡄⠀⢰⣾⠃⣼⣷⣤⣠⠜⣉⡇⠰⠉⠛⠋⢉⠠⡇⡟⢴⣿⣿⣿⣿⣰⣥⠞⠋⡄⠊⡗⠀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠠⡙⡖⣝⢧⡤⣤⡀⠀⠀⢛⣿⣷⡿⣳⣬⠰⡂⠈⢶⡷⢇⠡⢂⣘⢋⠄⣻⡿⣽⣿⣔⡟⠑⡀⡆⠀⢠⠘⢀⣧⠧⠚⠉⣿⣿⣿⣿⡍⠀⠀⣁⠐⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠣⣓⢿⡦⣝⠦⣂⡿⠟⣉⣰⢤⡀⠓⢦⡐⠀⠀⠺⠕⣎⣋⡘⢺⢿⣷⢎⣿⠀⠀⠈⠉⣿⣷⣮⣴⣿⣷⡄⠀⠀⡏⢻⣿⣿⣧⣍⣴⣏⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠈⠻⢶⣉⢭⣮⡓⣴⠋⠀⠀⠙⢷⣀⠋⣡⠐⠀⠀⠙⠧⠈⠢⣈⠟⢿⣿⣆⠀⢠⣸⣿⣿⣋⣿⣿⣿⣿⣶⣕⣱⣟⠋⠁⠀⠈⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠙⢿⡍⢃⠯⢤⡀⠀⠀⠸⢿⡇⢣⣶⠆⣐⠀⢀⠀⢳⡌⠛⢂⣴⡝⢌⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠫⡤⡆⠀⠀⣠⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⠫⣌⣓⠛⠲⠄⠀⠈⣷⢀⠙⢿⣿⣷⣤⡀⠀⠉⠲⠾⡿⡙⢾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠑⢦⣤⠶⣹⣦⡁⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠈⠙⢷⣦⡀⠈⣄⣻⠌⢀⠀⠁⢿⣿⣏⢷⣤⠣⣤⡁⣿⣵⡟⣿⣿⣿⣋⣾⣿⣿⣷⣅⠤⣀⣀⠴⣫⠂⠀⡙⣿⣿⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠙⢿⣦⡔⠤⠖⠌⠁⠀⣿⣿⣤⠮⠛⣛⠺⢹⣇⡀⡧⢸⠿⣿⣿⣿⣿⣿⣻⢣⠂⠀⠀⠀⢁⣀⠂⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠹⣷⠂⠰⡜⡀⢿⣿⡥⠤⢀⢤⡼⢿⣟⣯⣆⢿⡜⣿⣾⣿⣿⢿⡇⢇⠀⠀⠀⠀⢨⣇⡺⠋⠉⠛⢿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠲⠔⠟⡇⠸⣿⡟⢛⠓⠢⣤⢡⣾⣿⣈⣱⡳⣽⣯⣿⣞⡿⣿⣦⡑⢄⠀⢠⣣⣿⡷⡀⠀⠀⠀⢩⠤⠐⠠⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢙⣁⡈⠤⣽⣟⠘⢒⡶⡑⢌⠛⢿⣮⣝⣿⣻⣶⣟⣾⣽⢧⣟⣿⡄⠐⣷⣿⣿⣿⡑⠄⠀⠀⠀⢚⡀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠶⣉⠀⢀⠉⠑⠸⠋⠀⡀⢕⣌⣫⣿⣿⣟⡿⣼⣻⣽⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⡷⣄⠢⣀⠀⡓⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣬⣘⠚⠠⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡙⣿⣻⣿⣶⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢰⣿⣿⣿⣿⣿⣿⣷⣦⣕⡓⠂⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣶⣿⣳⢯⣿⣿⣿⡄

⠀⠀⠀⡄⠀⡄⠀⢸⡇⢸⡦⠀⠀⠀⡀⠀⠀⠀⠀⠉⢿⣿⣿⡯⠁⠸⠀⢹⢣⣿⡿⠟⠀⠀⠀⠀⠀⠵⡀⠀⠼⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡑⡰⠁⠀⢸⣇⢸⢢⠑⠤⠎⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡃⡈⡌⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠐⢁⡇⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠸⡏⡀⢧⠉⠰⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠋⢈⠀⠀⠀⠀⣠⢌⣀⣀⣀⡀⠈⢁⡞⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢇⢀⠇⠀⢠⡷⠃⢸⣧⣤⣽⣿⡿⡶⣫⡕⣄⠐⠒⠂⠤⣯⣿⢦⡪⠒⠀⠀⡾⡾⣷⣻⢻⡿⣿⣶⣿⡧⠀⠀⣀⡄⠀⠀⠀⠀ ⠀⠀⠸⠦⠚⠀⠀⠘⡇⠀⢸⣿⣿⠁⣿⣝⣥⣟⡮⡳⢆⠀⠀⠀⠈⢯⠜⠀⠀⠀⡰⡫⢊⢌⠨⢪⡝⣾⡿⣿⡇⢠⠊⢐⠁⠀⠀⠀⠀ ⠀⠀⠀⣠⡤⠄⠀⠀⡇⠀⡸⣿⣿⣢⣾⣿⣭⣣⡻⡮⣘⢳⢄⣀⣠⢾⢆⣀⣠⢔⣹⣾⡫⡫⡡⡫⣾⡿⣿⣿⡿⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣁⣲⠀⠀⠀⡇⢀⣩⣿⣿⣾⣿⢮⣗⢟⢟⢎⡲⡱⡠⡟⠗⢸⠸⣛⣣⠵⣵⣟⣎⡮⠪⣚⣝⢿⡟⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠁⠀⠀⠈⠇⠸⣿⣿⣿⣿⠏⢹⣠⠪⣫⢮⣗⡔⠊⠀⢤⢸⢸⡃⢚⡫⣋⣿⠫⣷⣿⡽⠿⠛⢹⣿⣟⠃⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⢠⢾⠁⡞⠀⠀⠀⠀⠹⣿⣿⣿⣶⢮⡳⠑⠡⠈⠀⠀⠀⣠⣾⢸⣸⣧⣛⣪⣝⠗⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠔⠀ ⠀⠠⠫⠸⠠⠀⠀⢀⡀⠀⠀⠏⣿⣿⡻⠛⠀⠀⠀⠀⣐⣧⣾⣿⣿⢸⣿⣿⠛⠁⠀⠀⠀⠀⠀⠔⣡⣿⡿⠃⠀⠀⠀⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⡏⠻⡿⠂⠢⣀⠀⠼⡿⣟⡛⠛⠻⣸⠟⠛⢛⡦⢔⡠⠤⣤⣔⠀⠈⠿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠹⣄⠀⢠⣾⢻⣗⢄⠙⢦⣥⣌⠁⢸⢊⡠⣀⣴⢊⣠⣶⡟⣸⣆⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⠀⠀⠀⠀⠀⣸⠋⠀⡘⠀⠀⢀⠌⠳⣿⣯⢆⠻⠥⠓⠃⡀⢨⠙⠚⠋⠁⡀⠘⢉⡹⠏⢠⡟⢨⠞⠁⠀⠀⢴⡀⠀⠀⠀⠀⠀⠠⢀ ⢸⡀⠀⠀⣠⣴⠏⠀⢀⡇⢀⠲⠉⠠⠀⣿⣯⡑⣷⡘⠓⡞⢀⠾⢠⣠⢀⢁⠈⡾⠖⣁⣴⠏⣠⡎⢀⡀⢀⢌⠔⠅⠀⠀⠀⠀⣠⡱⠐ ⠸⣶⡦⣾⠋⠀⠀⠀⡈⠧⠂⡘⠀⢂⣠⢾⣿⣷⣌⠳⣴⡽⠳⠷⡎⢻⢸⡌⠳⠶⣾⠟⢁⣾⣿⣇⡇⠀⠀⠸⠟⠀⠀⠀⣠⠎⠋⢘⠀ ⠀⠛⠛⢸⢲⠀⠀⠰⠀⠀⢀⣴⡶⢋⠔⣻⣿⣿⣿⣷⡈⠻⣦⢌⡧⣺⢅⣠⡴⠟⢁⣴⣿⣿⣿⣯⠻⣦⡀⠀⠀⠐⢠⡀⠁⠀⡔⠁⠀ ⠀⢀⣀⢸⠢⣁⣠⠆⠀⣠⣾⡜⡠⠁⣬⣿⣿⣿⣿⣿⣿⣶⣄⣉⠉⠉⠉⠉⣠⣴⣿⣿⣿⣿⣿⡀⠢⠙⣯⡒⢆⠁⠀⠀⠀⠀⠂⠀⠀

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